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Problem 3. (25 points). During the winter storm, you and your friends really wanted to reenact the famous scene from A Christmas Story Where Flick is tripledogdared to lick the school agpole, only to have his tongue freeze to the pole. Of course, it is unsafe to do this during a pandemic, so you waited until you were fully vaccinated. Let X denote the temperature on any given day (in Celsius), and Y the amount of hospital bills associated with licking the agpole on a given day (in thousands of dollars), whether due to freezing, catching an 1 _ infection, or anything else. The joint PDF of X and Y is i M if m E [710, 10] and y E [0, 10], _ 200 104 and 0 otherw1se. (a) (6) What is the marginal PMF for X ? (b) (6) What is the marginal PMF for Y? (c) (6) Are X and Y independent? (Explain your answer, do not just say yes or no.) (d) (7) What is the probability that the day you lick the agpole happens to be below freezing (X